Core-Shell structure using blender?
Creating the base meshes - step by step.

In this short tutorial I will only cover the creation of the base mesh without the materials. 


Add a single uv sphere, hit S followed by 2 to scale it. 
Select the vertices for the chunk you want to cut out by going into top view, hitting B and box-select the vertices. Double-check by rotating and selecting/deselecting additional vertices. 





Hit X and select "Faces" to delete the selected faces. 
Go into object mode, then go to the "Modifiers" Tab in the Properties Window, select "add modifier" and chose "Solidifiy".





Change "Thickness" in the Modifier settings to your liking.





Add another uv sphere and scale it until it fills the inner part of your solidified sphere (hit S followed by 1.6 to match the values I used in this example)